## PRP Records

### Probable Primes Top 10000

#### (295756 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 9001 2^338016-16335 101753 Stefano Morozzi 01/2023 9004 2^338010-19833 101752 Enzo Doria 06/2013 9002 2^338011+28665 101752 Stefano Morozzi 01/2022 9003 2^338010+89505 101752 Stefano Morozzi 05/2022 9005 2^338007+58985 101751 Stefano Morozzi 03/2022 9006 2^338008+109741 101751 Stefano Morozzi 03/2022 9007 2^338009+9527 101751 Stefano Morozzi 03/2022 9008 2^338007+14511 101751 Stefano Morozzi 05/2022 9009 2^338008+67957 101751 Stefano Morozzi 09/2022 9010 2^338009-11935 101751 Stefano Morozzi 12/2022 9011 2^338007-14199 101751 Stefano Morozzi 01/2023 9012 2^338005-75829 101750 Stefano Morozzi 12/2021 9013 2^338006-125055 101750 Stefano Morozzi 12/2021 9014 2^338006+5013 101750 Stefano Morozzi 01/2022 9015 2^338003+40269 101750 Stefano Morozzi 06/2022 9016 2^338006+166495 101750 Stefano Morozzi 06/2022 9017 2^338003-188551 101750 Stefano Morozzi 12/2022 9018 2^338006-118041 101750 Stefano Morozzi 02/2023 9019 2^338000+25113 101749 Stefano Morozzi 12/2021 9021 3^213215-76 101730 Lelio R Paula 09/2016 9020 23907^17998+17998^23907 101730 Hans Havermann 01/2019 9022 10^101728+154953 101729 Patrick De Geest 02/2020 9025 2^337930+63 101728 Lelio R Paula 07/2011 9023 10^101728-987654321 101728 Robert Price 12/2019 9024 10^101728-60741 101728 Patrick De Geest 02/2020 9026 2^337920+1869661 101725 Enzo Doria 05/2016 9027 2^337922+100280245065 101725 Paul Bourdelais 10/2021 9028 24116^16509+16509^24116 101715 Hans Havermann 01/2019 9029 (2^337875+3174)/2 101711 Stefano Morozzi 09/2020 9030 2^337859-19645 101706 Enzo Doria 05/2013 9031 2^337754+1869169 101675 Enzo Doria 05/2016 9032 (7*10^(2*50830+1)-9*10^50830-7)/9 101661 Robert Price 10/2023 9033 3*10^101657-37 101658 Robert Price 07/2018 9034 (31*2^337677-1)/593 101650 Lelio R Paula 03/2014 9035 11^97605-24 101646 Lelio R Paula 10/2016 9036 (83*10^101636+133)/9 101637 Robert Price 08/2021 9037 (2^337624+3606)/2 101635 Stefano Morozzi 09/2020 9038 8^112539-112539 101633 Robert Price 01/2014 9039 (2^337575+1818)/2 101620 Stefano Morozzi 02/2021 9040 (11*10^101613+61)/9 101614 Tyler Busby 01/2023 9041 25694^9003+9003^25694 101605 Hans Havermann 12/2018 9042 2^337515-19869 101603 Enzo Doria 06/2013 9043 2^337473+719 101590 Lelio R Paula 08/2011 9044 (2^337485-509203)/656647157 101585 Lelio R Paula 12/2013 9045 2^337452-108815 101584 Enzo Doria 03/2014 9046 2^337453+1185 101584 Lelio R Paula 09/2016 9047 (41*10^101583+319)/9 101584 Robert Price 06/2021 9048 2^337410-113561 101571 Enzo Doria 08/2014 9049 2^337387+855 101564 Lelio R Paula 09/2016 9050 2^337367-17295 101558 Lelio R Paula 09/2016 9051 2^337342-109035 101551 Enzo Doria 04/2014 9052 23703^19238+19238^23703 101548 Hans Havermann 12/2018 9053 (26*10^101537-167)/3 101538 Robert Price 10/2019 9054 2^337267-19 101528 Lelio R Paula 07/2011 9055 (2^337259+1766)/2 101525 Stefano Morozzi 09/2020 9056 (2^337257+2306)/2 101525 Stefano Morozzi 02/2021 9057 2^337222-340871 101514 Harrison Mesh 06/2022 9058 (2^337195+2646)/2 101506 Stefano Morozzi 09/2020 9059 2^337183-19989 101503 Enzo Doria 06/2013 9060 2^337149+72425 101492 Enzo Doria 04/2016 9061 24041^16642+16642^24041 101483 Hans Havermann 12/2018 9062 33982^969+969^33982 101482 Hans Havermann 12/2018 9063 2^337101-20241 101478 Enzo Doria 06/2013 9064 2^337035-20001 101458 Enzo Doria 06/2013 9065 (7*10^101456+89)/3 101457 Robert Price 08/2020 9066 2^337017-16995 101453 Lelio R Paula 09/2016 9067 (347^40448+1)/(347^512+1) 101451 Martin Hopf 12/2023 9068 (8677^25759-1)/8676 101445 Serge Batalov 06/2022 9069 2^336979-115315 101441 Enzo Doria 06/2015 9070 2^336970-20885 101439 Enzo Doria 06/2013 9071 2^336958+79 101435 Lelio R Paula 10/2009 9072 (1589^31687-1)/1588 101431 Serge Batalov 06/2022 9073 2^336942+169 101430 Lelio R Paula 10/2009 9074 (193929^19321-1)/(193929^139-1) 101428 Ryan Propper 11/2023 9075 (15185*2^336894-1)/7939 101416 Lelio R Paula 05/2015 9076 4*10^101415-89 101416 Robert Price 11/2018 9077 (14*10^101410-89)/3 101411 Robert Price 05/2020 9078 2^336871+257463 101409 Tony Prest / Never Odd Or Even 04/2016 9079 2^336871+318105 101409 Tony Prest / Never Odd Or Even 04/2016 9080 2^336871+1010813 101409 Tony Prest / Never Odd Or Even 04/2016 9081 2^336871+2302245 101409 Tony Prest / Never Odd Or Even 04/2016 9082 2^336871+389273 101409 Tony Prest / Never Odd Or Even 04/2016 9083 2^336871+1685475 101409 Tony Prest / Never Odd Or Even 04/2016 9084 2^336871+1068119 101409 Tony Prest / Never Odd Or Even 04/2016 9085 2^336871+586905 101409 Tony Prest / Never Odd Or Even 04/2016 9086 2^336871+674571 101409 Tony Prest / Never Odd Or Even 04/2016 9087 2^336871+707009 101409 Tony Prest / Never Odd Or Even 04/2016 9088 2^336871+1210299 101409 Tony Prest / Never Odd Or Even 04/2016 9089 2^336871+1921185 101409 Tony Prest / Never Odd Or Even 04/2016 9090 2^336871+2003973 101409 Tony Prest / Never Odd Or Even 04/2016 9091 2^336871+2656475 101409 Tony Prest / Never Odd Or Even 04/2016 9092 2^336871+2703023 101409 Tony Prest / Never Odd Or Even 04/2016 9093 2^336871+2704545 101409 Tony Prest / Never Odd Or Even 04/2016 9094 2^336871+2766801 101409 Tony Prest / Never Odd Or Even 04/2016 9095 2^336871+2127735 101409 Tony Prest / Never Odd Or Even 04/2016 9096 (2^336871+821089)/3 101408 Tony Prest / Never Odd Or Even 05/2016 9097 (2^336871+119567)/5 101408 Tony Prest / Never Odd Or Even 05/2016 9098 (2^336871+398161)/3 101408 Tony Prest / Never Odd Or Even 05/2016 9099 (2^336871+625889)/7 101408 Tony Prest / Never Odd Or Even 05/2016 9100 24097^16150+16150^24097 101405 Hans Havermann 12/2018 9101 2^336842+94065 101400 Lelio R Paula 09/2016 9102 (7*10^101395-1)/3 101396 Robert Price 08/2022 9103 (2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103 101378 Tony Prest / Never Odd Or Even 04/2016 9104 (2^336871+631971)/13/251/1601/294277/614362921/30324278867 101377 Tony Prest / Never Odd Or Even 04/2016 9105 (2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879 101374 Tony Prest / Never Odd Or Even 04/2016 9106 (2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489 101373 Tony Prest / Never Odd Or Even 04/2016 9107 (2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757 101373 Tony Prest / Never Odd Or Even 04/2016 9108 (2^336871+272895)/19/661/977572033/95853078653/520779768241 101373 Tony Prest / Never Odd Or Even 04/2016 9109 (2^336871+1023429)/2311/415873/991889/3630648341/207732189179 101373 Tony Prest / Never Odd Or Even 04/2016 9110 10^101369+203811 101370 Patrick De Geest 11/2016 9111 10^101369-99 101369 Lelio R Paula 09/2016 9112 (2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917 101363 Tony Prest / Never Odd Or Even 04/2016 9113 2^336701-113563 101358 Enzo Doria 08/2014 9114 89717!4-512 101351 Robert Price 11/2019 9115 2^336644-109023 101340 Enzo Doria 04/2014 9116 2^336601-21081 101327 Enzo Doria 06/2013 9117 (4*34^66153+227)/33 101312 Eric Chen 03/2023 9118 20^77869+63 101310 Lelio R Paula 09/2016 9119 (13*2^336523-1)/19 101304 Lelio R Paula 03/2014 9121 6^130179-137 101299 Lelio R Paula 10/2016 9120 (2^336506+lucasV(1,2,336506)+1)/2 101299 Mike Oakes 11/2016 9122 (24737*2^336485+1)/7285 101293 Lelio R Paula 07/2014 9123 (2^336448+9)/497405 101276 Lelio R Paula 12/2013 9124 2^336369-19753 101258 Enzo Doria 05/2013 9125 23842^17653+17653^23842 101253 Hans Havermann 11/2018 9126 2^336350-344291 101252 Enzo Doria 07/2015 9127 (17*10^101251-161)/9 101252 Robert Price 02/2021 9128 (56*10^101222-47)/9 101223 Robert Price 02/2019 9129 2^336243-108777 101220 Enzo Doria 03/2014 9130 (31*2^336189-1)/19 101204 Lelio R Paula 03/2014 9131 23535^19954+19954^23535 101202 Hans Havermann 11/2018 9132 (78557*2^336178+1)/1268757 101199 Lelio R Paula 07/2014 9133 U(618755)/22275181/747456041 101194 Serge Batalov 07/2024 9134 2^336150-20393 101192 Enzo Doria 06/2013 9135 23996^16473+16473^23996 101186 Hans Havermann 11/2018 9136 L(484301)/52304509/5481318719/94549115629 101185 Serge Batalov 07/2024 9137 2^336112-1865249 101180 Enzo Doria 03/2016 9138 2^336103-109015 101178 Enzo Doria 04/2014 9139 (2^336095+2078)/2 101175 Stefano Morozzi 09/2020 9140 2^336060+22201 101165 Enzo Doria 09/2023 9141 13^90809-96 101157 Lelio R Paula 10/2016 9142 26199^7258+7258^26199 101150 Hans Havermann 11/2018 9143 19^79098-30 101147 Lelio R Paula 10/2016 9144 19^79095+88 101144 Lelio R Paula 10/2016 9145 (30826*34^66040-59)/11 101143 Eric Chen 03/2023 9146 12401^24702-24702^12401 101117 Norbert Schneider 07/2022 9147 15^85976+32 101116 Lelio R Paula 10/2016 9148 2^335872-2776215 101108 Tony Prest / Never Odd Or Even 01/2019 9149 (3^211950+7)/28854513015920697088 101107 Lelio R Paula 11/2013 9150 (4^167933+17)/3 101106 Robert Price 02/2017 9152 2^335858+153 101104 Lelio R Paula 10/2009 9151 (2^335872-2776871)/5/5/479 101104 Tony Prest / Never Odd Or Even 01/2019 9153 (2^335872-2758787)/23/31/20809 101101 Tony Prest / Never Odd Or Even 01/2019 9154 (2^335839+2114)/2 101098 Stefano Morozzi 09/2020 9155 (2^335872-2795083)/3/3/113/283/148367 101097 Tony Prest / Never Odd Or Even 01/2019 9157 6^129918-35 101096 Lelio R Paula 10/2016 9156 (2*10^101096-107)/3 101096 Robert Price 11/2020 9158 3^211885-70 101095 Lelio R Paula 09/2016 9159 (29*2^335835-1)/550599 101093 Lelio R Paula 03/2014 9160 (2^335872-2794771)/3/5/5/61/232312440293 101093 Tony Prest / Never Odd Or Even 01/2019 9161 2^335818-20033 101092 Enzo Doria 06/2013 9162 2^335813-110083 101090 Enzo Doria 04/2014 9163 2^335804+2155 101088 Lelio R Paula 09/2016 9164 (2^335872-2756679)/7/7/7/13/31/4987/437653/8734021 101087 Tony Prest / Never Odd Or Even 01/2019 9165 2^335784-16145 101082 Enzo Doria 04/2013 9166 11^97051+62 101069 Lelio R Paula 10/2016 9167 3*10^101065+11 101066 Robert Price 07/2018 9168 27820^4293+4293^27820 101064 Hans Havermann 10/2018 9169 (2^335714+3750)/2 101060 Stefano Morozzi 01/2021 9170 (2^335690+1038)/2 101053 Stefano Morozzi 09/2020 9171 (2^335691-3)/26515 101049 Lelio R Paula 12/2013 9172 2^335658-94395 101044 Lelio R Paula 09/2016 9173 24514^13215+13215^24514 101024 Hans Havermann 11/2018 9174 2^335586+169 101022 Lelio R Paula 10/2009 9175 (56^57787-1)/55 101021 Paul Bourdelais 08/2017 9176 (2^335562+1258)/2 101014 Stefano Morozzi 09/2020 9177 2^335541+4849845 101008 Paul Bourdelais 04/2022 9178 (38*10^100999+169)/9 101000 Robert Price 11/2021 9179 (19*10^100997+737)/9 100998 Robert Price 07/2018 9180 47599!2+1024 100991 Robert Price 02/2015 9181 2^335468-18629 100986 Enzo Doria 05/2013 9182 2^335454-20961 100982 Enzo Doria 06/2013 9183 (2^335454+3258)/2 100982 Stefano Morozzi 02/2021 9184 10^100978+61 100979 Lelio R Paula 09/2016 9185 10^100978-156437 100978 Patrick De Geest 11/2016 9186 (2^335422+3114)/2 100972 Stefano Morozzi 09/2020 9187 (35*10^100970-89)/9 100971 Robert Price 02/2022 9188 (15*2^335417+1)/481 100970 Lelio R Paula 12/2013 9189 2^335403-1859167 100967 Enzo Doria 03/2016 9190 23599^18976+18976^23599 100962 Hans Havermann 10/2018 9191 6*10^100958+43 100959 Robert Price 07/2020 9192 9*2^335364-5 100956 Lelio R Paula 08/2014 9193 (7998^25867-1)/7997 100955 Serge Batalov 06/2022 9194 2^335349+72287 100951 Enzo Doria 04/2016 9195 2^335329+16095 100945 Lelio R Paula 09/2016 9196 232823#+233663 100937 Makoto Morimoto 10/2017 9197 (232823#+10141)/(10141*1674461) 100927 Makoto Morimoto 06/2019 9198 2^335237-20893 100917 Enzo Doria 06/2013 9199 2^335222-19337 100912 Enzo Doria 05/2013 9200 2^335222-109985 100912 Enzo Doria 04/2014 9201 2^335182-17237 100900 Enzo Doria 05/2013 9202 (2^335107+1634)/2 100877 Stefano Morozzi 09/2020 9203 2^335043-16737 100858 Enzo Doria 05/2013 9204 (21181*2^335049+1)/1343811 100858 Lelio R Paula 07/2014 9205 2^335038-20633 100857 Enzo Doria 06/2013 9206 2^335031+1873373 100855 Enzo Doria 06/2016 9207 23489^19650+19650^23489 100847 Hans Havermann 10/2018 9208 3^211354-8816 100842 Enzo Doria 05/2014 9209 2^334984-112757 100841 Enzo Doria 06/2014 9210 (746*10^100827+1)/9 100829 Robert Price 03/2020 9211 29451^2648+2648^29451 100809 Hans Havermann 09/2018 9212 25583^8716+8716^25583 100806 Hans Havermann 08/2018 9214 2^334857+48527 100803 Lelio R Paula 08/2011 9213 12^93406+29 100803 Lelio R Paula 10/2016 9215 28780^3179+3179^28780 100796 Hans Havermann 09/2018 9216 (5*2^334825+1)/47 100792 Lelio R Paula 12/2013 9217 (328^40063-1)/327 100791 Serge Batalov 06/2022 9218 2^334809-13 100788 Lelio R Paula 04/2011 9219 (3552^28387-1)/3551 100784 Serge Batalov 06/2022 9220 (82*10^100780-1)/9 100781 Robert Price 12/2014 9221 31395^1622+1622^31395 100780 Hans Havermann 09/2018 9222 (2^334779+47)/5 100778 Lelio R Paula 12/2013 9223 2^334751+2049 100771 Lelio R Paula 09/2016 9224 13^90443-98 100749 Lelio R Paula 10/2016 9225 (2^334674+3190)/2 100747 Stefano Morozzi 09/2020 9226 (2^334651+1050)/2 100740 Stefano Morozzi 09/2020 9227 (7*10^100737+71)/3 100738 Robert Price 05/2018 9228 (24737*2^334628+1)/3 100737 Lelio R Paula 07/2014 9229 15^85639-28 100720 Lelio R Paula 10/2016 9230 27068^5259+5259^27068 100718 Hans Havermann 08/2018 9231 2^334562+577294575 100711 Lelio R Paula 09/2016 9232 4*3^211077-5 100710 Lelio R Paula 08/2014 9233 2^334524+145 100702 Lelio R Paula 07/2009 9234 (2^334451+714)/2 100680 Stefano Morozzi 09/2020 9235 27648^4375+4375^27648 100666 Hans Havermann 09/2018 9236 (1017*2^334391-1)/3535 100662 Lelio R Paula 05/2015 9237 (2^334309+3122)/2 100637 Stefano Morozzi 09/2020 9238 2^334294-113111 100633 Enzo Doria 07/2014 9239 25581^8582+8582^25581 100626 Hans Havermann 08/2018 9241 6^129308-17723 100622 Enzo Doria 03/2013 9240 (19*10^100627+287)/9/292157 100622 Alfred Reich 11/2022 9242 6^129305+95 100619 Lelio R Paula 10/2016 9243 2^334244-1167 100618 Lelio R Paula 09/2016 9244 (2^334233+3066)/2 100614 Stefano Morozzi 09/2020 9245 (76*10^100611+77)/9 100612 Robert Price 10/2019 9246 7*10^100606-93 100607 Robert Price 08/2020 9247 (26*10^100566+49)/3 100567 Robert Price 08/2019 9248 (21*2^334050+1)/935 100558 Lelio R Paula 12/2013 9249 24885^10984+10984^24885 100555 Hans Havermann 07/2018 9250 (1351^32119-1)/1350 100551 Serge Batalov 06/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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